Success of sky-polarimetric Viking navigation: revealing the chance Viking sailors could reach Greenland from Norway

Abstract

According to a famous hypothesis, Viking sailors could navigate along the latitude between Norway and Greenland by means of sky polarization in cloudy weather using a sun compass and sunstone crystals. Using data measured in earlier atmospheric optical and psychophysical experiments, here we determine the success rate of this sky-polarimetric Viking navigation. Simulating 1000 voyages between Norway and Greenland with varying cloudiness at summer solstice and spring equinox, we revealed the chance with which Viking sailors could reach Greenland under the varying weather conditions of a 3-week-long journey as a function of the navigation periodicity Δt if they analysed sky polarization with calcite, cordierite or tourmaline sunstones. Examples of voyage routes are also presented. Our results show that the sky-polarimetric navigation is surprisingly successful on both days of the spring equinox and summer solstice even under cloudy conditions if the navigator determined the north direction periodically at least once in every 3 h, independently of the type of sunstone used for the analysis of sky polarization. This explains why the Vikings could rule the Atlantic Ocean for 300 years and could reach North America without a magnetic compass. Our findings suggest that it is not only the navigation periodicity in itself that is important for higher navigation success rates, but also the distribution of times when the navigation procedure carried out is as symmetrical as possible with respect to the time point of real noon.

Sensitivity and robustness of sky-polarimetric Viking navigation: Sailing success is most sensitive to night sailing, navigation periodicity and sailing date, but robust against weather conditions

“…During a given time period τ, the simulated Viking ship moved in a constant direction along a straight line with a constant sailing speed w until the navigator determined the new sailing direction. In the simulation, the time segment τ was chosen randomly with a uniform distribution from the interval Δ t − Δ t /6 ≤ τ ≤ Δ t + Δ t /6, where Δ t is the navigation periodicity (= the elapsed time since the last navigation) [ 34 ]. Before each run, Δ t was randomly selected from the following range: 0.5 hour ≤ Δ t ≤ 6 hours.…”

“…[ 33 ] also interpreted the Uunartoq fragment as a twilight board and demonstrated in a field experiment how the Viking sun-compass could have been used with sunstones before and after sunset. Using celestial polarization patterns and psychophysically measured errors, Száz and Horváth [ 34 ] revealed with computer simulations the chance that Vikings could reach Greenland.…”

“…After these studies the logical question of the sensitivity or robustness of SPVN has arisen. Using an improved version of the software of Száz and Horváth [ 34 ], in this work we investigate the sensitivity/robustness of the success of SPVN to the following relevant sailing, meteorological and navigational parameters: sunstone crystal type, sailing date, navigation periodicity, sailing or staying at night, dominance of strongly, medium or weakly cloudy skies, and cloudiness changeability. Randomly varying these parameters in the simulations of Viking voyages, we determined those parameters which have strong and weak influences on the success of SPVN.…”

Psychophysical study of the moon illusion in paintings and landscape photos

“…The authors of this paper were not among these 10 participants. In our earlier similar psychophysical experiments, we used also 10 test persons [34–41]. For every x 1 , x 2 , … , x n data series, we calculated the average x and its standard deviation σ as follows: x=1nfalse∑i=1i=nxi,σ=∑i=1i=nfalse(xi−xfalse)2n} …”

A Bio-Inspired Polarization Sensor with High Outdoor Accuracy and Central-Symmetry Calibration Method with Integrating Sphere

“…The authors determined the accuracy [22] of hypothetical sky-polarimetric Viking navigation for 1080 different sky conditions that were characterized by parameters such as solar elevation and cloudiness [23]. A simulation based on a large amount of actual data [23], obtained using imaging polarimetry, shows that Viking sailors could have travelled to Greenland from Norway using polarization information [24]. Furthermore, the angle algorithm has also been improved.…”